Triangle Sum Theorem activity worksheet with answer key.

The image you provided appears to be a worksheet related to the Triangle Sum Theorem, which states that the sum of the interior angles of a triangle is always 180 degrees. The task involves solving for missing angles in various triangles, using this theorem.

Explanation of the Triangle Sum Theorem:

- For any triangle, the sum of its three interior angles is always 180°.
- If two angles are known, the third angle can be found using the formula:
\[
\text{Third Angle} = 180^\circ - (\text{Angle 1} + \text{Angle 2})
\]

Steps to Solve the Problem:

1. Identify the given angles in each triangle.
2. Use the Triangle Sum Theorem to find the missing angle.
3. Follow the flowchart or sequence provided in the worksheet to solve step by step.

Example Walkthrough:

Let’s assume one of the triangles in the worksheet has the following angles:
- One angle is \( 50^\circ \).
- Another angle is \( 60^\circ \).
- The third angle is unknown.

Using the Triangle Sum Theorem:
\[
\text{Third Angle} = 180^\circ - (50^\circ + 60^\circ) = 180^\circ - 110^\circ = 70^\circ
\]

General Approach for Each Triangle:

For each triangle in the worksheet:
1. Add the given angles.
2. Subtract the sum from 180° to find the missing angle.
3. Use the calculated angle to proceed to the next triangle as indicated by the arrows in the flowchart.

Final Answer:

Since the exact numerical values of the angles in the worksheet are not provided in your question, I cannot compute specific answers. However, the general method to solve each triangle is as described above. If you provide the specific angles from the worksheet, I can calculate the missing angles for you.

If you need further clarification or assistance with specific triangles, feel free to share the details!

Final Answer: Use the Triangle Sum Theorem (\(180^\circ - \text{sum of given angles}\)) to find the missing angles in each triangle.

$$
\boxed{\text{Use the Triangle Sum Theorem to solve each triangle.}}
$$